Show commands:
SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 259896.bx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
259896.bx1 | 259896bx2 | \([0, 1, 0, -2564, -12720]\) | \(61918288/33813\) | \(1018384803072\) | \([2]\) | \(368640\) | \(0.99489\) | |
259896.bx2 | 259896bx1 | \([0, 1, 0, 621, -1254]\) | \(14047232/8619\) | \(-16224267696\) | \([2]\) | \(184320\) | \(0.64831\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 259896.bx have rank \(1\).
Complex multiplication
The elliptic curves in class 259896.bx do not have complex multiplication.Modular form 259896.2.a.bx
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.